Fit all of your new tessellation pieces together to create a beautiful, puzzle-like work of art! Very important -be sure to maintain the same orientation of your cut-out shape every time you tape it!ħ. Repeat Step 4 and Step 5 for each of your remaining squares. Tape your cut-out shape to that side of the square, lining up the long flat edges.Ħ. Rotate the square by 90˚(one corner in either direction) so that you have a fresh, flat, un-cut edge of the square facing you. Take one of your squares and cut out your tracing.ĥ. You should now have four squares of paper, each with your shape traced out in the same way.Ĥ. Ensure that your oddly-shaped cut-out is facing the same way every time you trace it. Repeat for each of the remaining three squares. Trace your cut-out onto the square with your pencil.ģ. Line your oddly-shaped cut-out on top of a second square of paper, lining up the long edges. (So if you start cutting from the bottom side of the square, make sure your scissors finish cutting on the bottom side of the square!)Ģ. Take one square piece of paper and cut a weird shape out of one side of the square. Start with five squares of paper that are the same size.ġ. Great for beginner cutters, and a great next step into more complex tessellation making.Ġ. Do they fit together? Try creating more complex shapes, like fish, flowers, or even dinosaurs! Now try drawing that shape again immediately next to the first shape. ![]() Step it up: Ready for a harder challenge? Skip Step 2 and just try drawing a shape on a piece of paper. If your shapes are fitting together perfectly, keep drawing them in each row until your entire sheet is filled up.ĥ. Do they fit together perfectly? What if you draw a third shape immediately next to the second shape? Do they still fit together perfectly?Ĥ. Draw that shape again immediately next to your first shape. In one row, draw a simple shape that spans the entire height of the row (see image above), such as a square, triangle, a lopsided rectangle (parallelogram), or other shape of your choice. Divide the paper up into equal width rows (or columns) about 3-4 rows for a small sheet will work very well.ģ. ![]() We recommend starting with half of a regular 8.5" x 11" white sheet of paper.Ģ. Start with a piece of paper and a pencil. Lizard tiles by Ben Lawson.No cutting is involved for this starter tessellation design, making it a great starting project for younger artists.ġ. Hexagonal and rhombic tessellations from Wikimedia Commons. Triangular tessellation from pixababy.If you want to try a more complicated version, cut two different squiggles out of two different sides, and move them both.Color in your basic shape to look like something - an animal? a flower? a colorful blob? Add color and design throughout the tessellation to transform it into your own Escher-like drawing. The shape will still tessellate, so go ahead and fill up your paper.Then move it the same way you moved the squiggle (translate or rotate) so that the squiggle fits in exactly where you cut it out. On a large piece of paper, trace around your tile. Tape the squiggle into its new location.It’s important that the cut-out lines up along the new edge in the same place that it appeared on its original edge.You can either translate it straight across or rotate it. Cut out the squiggle, and move it to another side of your shape.Draw a “squiggle” on one side of your basic tile.The first time you do this, it’s easiest to start with a simple shape that you know will tessellate, like an equilateral triangle, a square, or a regular hexagon. Here’s how you can create your own Escher-like drawings. Tessellations are often called tilings, and that’s what you should think about: If I had tiles made in this shape, could I use them to tile my kitchen floor? Or would it be impossible? The first two tessellations above were made with a single geometric shape (called a tile) designed so that they can fit together without gaps or overlaps. So we’ll focus on how to make symmetric tessellations. ![]() It’s actually much harder to come up with these “aperiodic” tessellations than to come up with ones that have translational symmetry. The Penrose tiling shown below does not have any translational symmetry. Many tessellations have translational symmetry, but it’s not strictly necessary. The idea is that the design could be continued infinitely far to cover the whole plane (though of course we can only draw a small portion of it). \)Ī tessellation is a design using one ore more geometric shapes with no overlaps and no gaps.
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